L. Schimmele

Investigation of muon states in silicon and germanium by field-quenching and RFμSR

The temperature dependence of the three states of positive muons in the semiconductors with diamond structure (μ+ in diamagnetic statesμd and paramagnetic muonium Mu and Mu*) have been investigated on six Si (pure, B and P doped) and four Ge (ultrapure, CZ-grown undoped, Ga and Sb doped) single crystals by longitudinal field-quenching and radio-frequencyμ+SR. Clear evidence for the transition Mu* →μd is found. The influence of light-induced charge-carriers is shown to be quite different in p- and n-type material.

Investigation of muon-state dynamics in silicon by longitudinal field-quenching and radio-frequency μ+ spin resonance

The two paramagnetic muon states-normal and anomalous muonium-and the diamagnetic muon states have been investigated in different monocrystalline silicon samples (intrinsic, boron-, phosphorus-, or arsenic-doped, float-zone or Czochralski-grown) between 6K and 800K by means of longitudinal field-quenching (LFQ) and radio-frequency μ + spin resonance (RFμSR). The LFQ data can be described consistently by coupled equations of motion for the muonium spin systems if spin exchange processes as well as transitions between different muon states are taken into account. It is shown that the initial formation probabilities of the different muon states, the ionization rate of the anomalous muonium, and the electron spin exchange rates depend strongly on the charge carrier densities. These results are in agreement with the RFμSR data obtained on the same samples if the different time scales of RFμSR and LFQ experiments are taken into account. At temperatures above 300 K both RFμSR and longitudinal relaxation results appear to indicate reversible ionization of normal muonium.

Radio-frequency muon spin resonance (RFμSR) experiments on condensed matter

In this paper we present an overview of the radio-frequency muon spin resonance (RFμSR) technique, an analogue to continuous-wave NMR, and an introduction to time-integral (TI) and time-differential (TD) RFμSR on muons in diamagnetic or in paramagnetic environments. The general form of the resonance line for TI-RFμSR as well as the expression for the time-dependence of the longitudinal muon spin polarization at resonance are given. Since RFμSR does not require phase coherence of the muon spin ensemble, this technique allows us to investigate muon species that are generated by transitions from, or in the course of reactions of, a precursor muon species even if in transverse-field (TF) μSR measurements the signal is lost due to dephasing. This ability of RFμSR is clearly demonstrated by measurements on doped Si. In this example, at low temperatures, a very pronounced signal from a muon species in diamagnetic environment has been found in RFμSR measurements, whereas in TFμSR experiments only a very small signal from muons in diamagnetic environment could be detected and a large fraction of the implanted muons escaped detection. These findings could be interpreted in terms of the delayed formation of a diamagnetic muonium-dopant complex, and, due to the large diamagnetic RFμSR signal, the RFμSR technique is a unique tool to study how the variation of parameters and experimental conditions such as illumination affects formation and behavior of these complexes. First results obtained on illuminated boron doped Si are reported. However, as illustrated by the example of experiments on the muonated radical in solid C60, results from conventional TI-RFμSR cannot always be interpreted unambiguously since different parameters, namely the fraction of muons forming the investigated muon species, the longitudinal and the transverse relaxation rates, have similar effects on height and shape of the RFμSR resonance line. These ambiguities, however, may be resolved by collecting time-differential data. With this extension RFμSR becomes a very powerful complementary method to TFμSR in the studies of dynamic effects.

μ+SR study of vacancies in thermal equilibrium in ferromagnets

Muon spin precession frequencies and transverse relaxation rates have been measured on demagnetized iron, cobalt, and FeCo alloys (3 at%–50 at% Co) between room temperature and the Curie temperatureTc. The increase of the relaxation rate in iron between 930 K and 1010 K could be quantitatively attributed to the trapping of positive muons by vacancies in thermal equilibrium, resulting in an enthalpy of monovacancy formation ofH1VF=(1.7±0.1) eV. the smallest vacancy concentrations detected are = 10−8.

What can we learn about critical magnetic phenomena from muon spin rotation experiments

Measurements of the spin precession frequencies ωμ and transvers relaxation rates Γ2 of positive muons (μ+) magnetic phase of several iron-cobalt alloys and coabalt, and in amorphous Feo.91Zr0.09 alloys are discussed with particular reference to the influence of critical phenomena on ωμ and Γ2. Although the temperature dependence ωμ(T) is well described by scaling law ωμ ∝ (Tc−T)β′ where α′ varies strongly with the co concentration in the FeCo alloys, it is shown that the exponent α′ is not identical to the static scalling parameter β describing the critical behaviour of the spontaneous magnetization M. In paramagnetic iron we find Γ2∝(T-Tc)0.72, which is attributed to the effect of dynamical spin fluctuations on the μ+. Due to the apparent difference between the temperature dependence of ωμ and that of M below Tc the frequency shifts observed in the paramagnetic regime are probably not directly proportional to the magnetic susceptibility. In amorphous Fe0.91Zr0.09 allosy frequency shifts and transverse relaxation rates are found up to nearly 2 Tc. Due to the shape of the Fe0.91Zr0.09 sample, demagnetization inhomogeneities certainly play an important rôle.

Positive mouns in iron: Dipolar fields at tetrahedral sites and jump frequencies at low temperatures

On polycrystalline and monocrystalline iron muon-spin precession frequencies and transverse relaxation rates have been measured down to 0.5 K. In the polycrystalline sample two distinct precession frequencies were observed at and below 1.4 K. They are attributed to the different dipolar fields at magnetically inequivalent tetrahedral interstices seen by muons moving locally around impurities. By contrast, in monocrystalline iron we observed only one precession frequency in monocrystalline iron with a damping rate which increased with decreasing temperature down to 0.5 K. We attribute the difference between the monocrystalline and the polycrystalline sample to different impurity contents. The single-crystal data are discussed in terms of μ+ diffusion by hopping between interstitial sites of tetragonal symmetry. The answer to several open questions is expected from an extension of the measurements to lower temperatures.

Low-temperature quantum diffusion of light particles: the domains of the various mechanisms in the static-energy-asymmetry-temperature plane

The motion of a light particle in a solid coupled to conduction electrons and/or phonons is investigated within the framework of a two-state model, which may be taken as representing the particle ground states in two neighbouring potential wells. With regard to the coupling of the particle to phonons, an important distinction arises between (i) special two-phonon processes, termed diphonon processes, which result from nonlinear particle-lattice coupling and which may give rise to quasielastic phase-destroying scattering and (ii) essentially inelastic processes which may arise from linear as well as from nonlinear particle-lattice coupling. An important parameter affecting particle motion is the static energy shift e between the particle ground states in the two wells. Under favourable conditions it may be experimentally controlled within certain limits. The two-state model allows us to estimate reliably the boundary in the e-T plane separating the regimes of incoherent hopping from that of coherent bandlike motion, and to discuss its dependence on the particle mass and the coupling parameters. Within the regime of incoherent motion a number of subregimes may exist. The situation becomes particularly interesting if a condensation of the electron system takes place, as in the case of a Bardeen-Copper-Schriefer superconductor. Then domains have to be distinguished in which the hopping rates are dominated by either quasiparticle coupling, diphonon processes, one-phonon processes, Cooper-pair breaking, coupling to normal-conducting electrons, or multiphonon-assisted processes. In the series of light particles carrying one positive elementary charge, which includes the positive muon (μ + ) and the nuclei of the hydrogen isotopes, the range of validity of the two-state description extends to rather high temperatures for the μ * but only to considerably lower temperatures for the heavier particles. Nevertheless, for protons the limiting temperature can be almost as high as the Debye temperature. Towards low temperatures the validity of the two-well description of unrestricted particle motion in a crystal is limited by the onset of coherent motion.

Evidence for a novel muon species in crystalline silicon

Abstract Investigations of positive muons (μ+) in crystalline silicon employing the longitudinal field-quenching (LFQ) technique give strong evidence for the existence of a novel paramagnetic muon species with a small anisotropic hyperfine interaction. It adds to the list of known muon species, i.e., normal and anomalous muonium and the diamagnetic muon species. The signatures of the novel species are found in intrinsic but not in doped samples (dopant concentration about 1016 cm−3). The novel species is not formed promptly but results from a reaction in which normal muonium transforms into the novel species. The reaction rate constant at 10 K was found to be about 106 s−1. The hyperfine coupling of the novel paramagnetic muon species corresponds, after rescaling, to that of a hydrogen center termed VH, which has been discovered recently by Bech Nielsen et al. (Phys. Rev. Lett., 79, 1997, 1507) and which has been attributed to hydrogen trapped in vacancies. The LFQ data are tentatively interpreted in terms of trapping of normal muonium in vacancies that are created during the slowing-down of implanted muons close to the end of their stopping tracks.

Muon state dynamics in germanium and silicon

The dynamics of the various muon states (paramagnetic states muonium Mu and anomalous muonium Mu*, diamagnetic states μd) were studied by means of radio‐frequency μ+ spin resonance (RFμSR), longitudinal field‐quenching (LFQ), and transverse μ+ spin rotation (TFμSR) in an undoped high‐purity and a gallium‐doped germanium single crystal in the temperature range 3.5–320 K.In boron‐doped Si the influence of photo‐induced charge carriers leads to muon state dynamics which is fundamentally different from the one observed if majority carriers are generated thermally. LFQ measurements have been performed in the temperature range 55–320 K in order to study these dynamic processes.

Influence of elastic strain onμ+ SR in α-iron single crystalsSR in α-iron single crystals

The spin-precession frequencies and the transverse spin relaxation rates of positive mouns (μ+) have been measured on two elastically strained α-Fe single crystal platelets as well as on an unstrained reference α-Fe crystal at temperatures down to 2.7 K in applied magnetic field 0≤Bappl≤3 T. The drastic effects of the strains may be qualitatively understood in terms of their influence on both the magnetic domain structure and theμ+ energies at the various interstitial sites. This leads to the conclusion that at low temperaturesμ+ in α-Fe occupy configurations related to octahedral interstitials with dipolar fieldBdip=0.70 T.